# Conceptually, what is the Message frequencies affect on the FM signals rest frequency

Context: Frequency modulation via a Voltage Controlled Oscillator (VCO)

If I take a message signal of frequency $F_{mes}$ and use it to generate a FM signal with a VCO, which has a rest frequency of $F_r$ and a deviation frequency of $F_d$, what is the relationship between the rest frequency $F_r$ and the message frequency $F_{mes}$?

Does the frequency modulation follow: $$F_{FM} = (F_{mes}\times F_r)+F_d$$ Or am I completely off?

My reasoning is that the change in the magnitude of the message signal amplitude is proportional to the change in the deviation frequency. However, increasing the frequency of the message signal will increase the frequency of the deviation frequency being changed, therefore it alters the base rest frequency to a new rest frequency value that the deviation frequency can then move away from due to different message signal amplitude values being input.

I think you are confusing your signal frequency with your signal envelope. FM radios adjust the frequency by the envelope not the frequency of the signal.

$F_{FM} = F_R + F_{D}*V_{signal}/VMAX_{signal}$

The rest frequency will stay the same.

However, if your signal has a dc component, it may appear to the receiver that the rest frequency is something different.

• You're right, I have said the message frequency rather than message signal in the bottom paragraph, sorry. – Brent Apr 12 '17 at 13:17
• Thank you very much for your answer. So the equation you reference is for the instantaneous frequency of the modulated signal? And your saying if there is a DC offset the $V_{signal}$ will be seen as altered and therefore distort the perceived instantaneous frequency of the FM signal? – Brent Apr 12 '17 at 13:24
• If you are sending a DC signal it may be filtered out by the receiver as a base frequency error. Most do to allow for errors in the tuned vs expected frequency. – Trevor_G Apr 12 '17 at 13:49

Carson's rule for the bandwidth of an FM signal is:

$$Signal Bandwidth \approx 2\times(F_D+F_M)$$

Where FD is the frequency deviation and FM is the modulating frequency

So the bandwidth used is independent of the carrier frequency but depends upon both the maximum frequency deviation and the maximum frequency of the data signal.

This isn't exact but is normally close enough that it's not normally worth the additional effort to get the exact number.